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The classical Mountain Pass Lemma of Ambrosetti-Rabinowitz has been studied,extended and modified in several directions, notable examples would certainlyinclude the generalization to locally Lipschitz functionals in K.C. Chang,analysis of the structure of the critical set in the mountain pass theorem byHofer and Pucci-Serrin and Tian, the extension by Ghoussoub-Preiss to closedsubsets in a Banach space, and variations found in the recent Peral . In thispaper, we utilize the generalized gradient of Clarke and Ekeland's variationalprinciple to generalize the Ghoussoub-Preiss's Theorem in the setting oflocally Lipschitz functionals.

Generalized Mountain Pass Lemma Related with a Closed Subset and Locally Lipschitz Functionals